The political failure of the former justice secretary, Ken Clarke's, sentencing reforms means the prison and probation services are set to miss targets for deep spending cuts set by the Treasury, Whitehall's spending watchdog has warned.

The National Audit Office says that official hopes of saving money by reducing the record prison population of 86,000 in England and Wales by 6,000 and closing older, more expensive prisons have been dashed. Jail numbers are now not expected to fall significantly over the next few years.

The Whitehall spending watchdog also warns that prison and probation budgets could come under further pressure from even slight changes in demand and would be placed in even deeper difficulties by any repeat of last summer's riots or a more punitive approach by the courts.

The problem is likely to lead to the new justice secretary, Chris Grayling, pushing through a round of spending cuts and accelerating the move to greater privatisation in prisons and probation.

A National Audit Office report published on Tuesday also discloses that the national offender management service, the agency that runs prisons and probation, faces an unexpected bill of up to £35m in 2012/13 to resolve problems in two case management and offender risk assessment computer projects. Both have been designated as "high risk" needing a high degree of scrutiny.

"The national offender management service is less than halfway through its cost cutting programme but is already lagging behind its target to curb spending by £884m before March 2015," said Margaret Hodge, chair of the Commons public accounts committee. "This figure must be hit if the Ministry of Justice is to stand any chance of achieving £2bn annual savings by the same deadline."

The NAO says that Clarke's sentencing reform programme, which included sentence discounts of up to 50% for early guilty pleas, was designed to reduce the size of the prison population by 6,000 by 2015. But Clarke was forced to drop key elements of the package last year after a row over his remarks over the sentencing of rape cases.

The Whitehall spending watchdog says the price of that decision was the loss of £130m of potential savings. The sentencing reform package is now expected to lead to only 2,000 fewer prison places, mainly as a result of changes to remand legislation, but the Treasury has not reduced targets for savings. "Given the loss of these reforms, the prison population is now unlikely to fall significantly over the next few years. This limits the agency's plans to close older, more expensive, prisons and bring down costs," says the NAO. It reports that this year's target to find £246m in savings is already "challenging" as it is currently projected to spend £32m more than its budget. It also faces a £66m shortfall in the £122m it needs to fund early staff departures over the next two years.